Berry-phase treatment of the homogeneous electric field perturbation in insulators - art. no. 155107

A perturbation theory of the static response of insulating crystals to homo geneous electric fields that combines the modem theory of polarization (MTP ) with the variation-perturbation framework is developed at unrestricted or der of perturbation. First, we address conceptual issues related to the def inition of such a perturbative approach. In particular, in our definition o f an electric-field-dependent energy functional for periodic systems, the p osition operator appearing in the perturbation term is replaced by a Berry- phase expression, along the lines of the MTP. Moreover, due to the unbound nature of the perturbation, a regularization of the Ferry-phase expression for the polarization is needed in order to define a numerically stable vari ational procedure. Regularization is achieved by means of discretization, w hich can be performed either before or after the perturbation expansion. We compare the two possibilities and apply them to a model tight-binding Hami ltonian. Lowest-order as well as generic formulas are presented for the der ivatives of the total energy, the normalization condition, the eigenequatio n, and the Lagrange parameters.